Concepts – Maverick Philosopher

The Concept GOD as a Limit Concept

The concept GOD is the concept of a being that cannot be constituted in consciousness in Husserl's sense of 'constitution,' a being that cannot be a transcendence-in-immanence, but must be absolutely transcendent, transcendent in itself, not merely for us. It follows that there cannot be a phenomenology of God. At best, there can be a phenomenology of such of our experiences as purport to be of or about God.

We know that the concept GOD is the concept of something absolutely transcendent, and we know this by purely conceptual means. We have the concept GOD and we analyze it: we simply unpack its meaning. Whatever the origin of this concept, it is there in us and available for analysis. Of course, we cannot learn by conceptual analysis that God exists, but we can know something about what God cannot be like, if he does exist. We can know, for example, that God, if he exists, is not a concept. No surprise here, and nothing that distinguishes God from my chair, since my chair is not a concept either. (One cannot sit on a concept.) The difference between the concept CHAIR and the concept GOD is the difference between an ordinary concept and a limit concept (Grenzbegriff).*

This is the distinction between those concepts that can capture (mirror, represent) the essences or natures of the things of which they are the concepts, and those concepts that cannot. Call the first type ordinary concepts and the second limit concepts. Thus the concept CUBE captures the essence of every cube, which is to be a three-dimensional solid bounded by six square faces or sides with three meeting at each vertex, and it captures this essence fully. The concept HELIOTROPIC PLANT captures, partially, the essence of those plants that exhibit diurnal or seasonal motion of plant parts in response to the direction of the sun. Concepts are mental representations. Essences are extra-mental.

Now the concept GOD cannot be ordinary since this concept cannot capture the essence of God. For (i) in God essence and existence are one, and (ii) there is no ordinary concept of existence.

Ad (i). That in God essence and existence are one follows from the fact that nothing could count as the Absolute if it were a composite of essence and existence. And we know by conceptual analysis that God is the Absolute: the concept GOD is the concept of 'something' absolute. This is the case whether or not God exists.

Ad (ii). When I say that there is no ordinary concept of existence, I mean that there is no ordinary (non-limit) concept that is adequate to existence. (There are bogus concepts of existence such as Quine's.) There is no ordinary (non-limit) concept of existence because the existence of a thing, as other than its essence, cannot be conceptualized. Why not?

This is because each existing thing has its own existence. Thus the existence of Al is Al's existence, the existence of Bob is Bob's, and the existence of Carla is Carla's. For the existence of a thing is that which makes that very thing exist. Existence cannot be a property like being human, being sentient, being sunburned. These properties are multiply instantiable; existence, however, is not multiply instantiable. There are no instances of existence.

Now if each thing has its own existence, then existence is implicated in the irreducible singularity of each existing thing. Irreducible singularity, in turn, cannot be conceptualized by minds like ours which trade only in the general and multiply instantiable. It's an Aristotelian point. If Aristotle wrote in Latin it would go: individuum qua individuum ineffabile est. The individual as such, the singular as such, is ineffable and cannot be conceptualized. The Peripatetic tells us that science is never of the particular as particular but only of the particular as exhibiting general or repeatable features. The particular as such is unrepeatable. But of course there are no individuals (particulars) bare of properties. Every finite individual is a this-such. This is a law of metaphyica generalis. So, while the individual as individual cannot be conceptualized, the individual as bearer of properties can be conceptualized as an instance of those properties. If I think of Mary as an instance of lovable properties, then I abstract from the haecceity (thisness) that makes her different numerically from her indiscernible twin Sherry. So if I love Mary precisely and only as an instance of lovable properties, then it will make no difference to my so loving her whether Mary or Sherry is its object. It will, however, make a difference to Mary. "I want that you should love me for what makes me me, and not for what I have in common with her!" I explain this all in great detail in Do We Love the Person or Only Her Qualities?

The crucial point here is that when we think of an individual as an instance of properties, we abstract from (leave out of consideration) the individual's thisness and its existence. I am not saying that the existence and the thisness of a concrete individual are one and the same; I am saying that that they go together as a matter of metaphysical necessity.

Ad (i + ii). In God there is no real distinction between existence and nature. That was the first point. The second was that no ordinary (non-limit) concept captures the individuality of the thing of which it is the concept. Therefore, since God is (identically) his nature, there can be no ordinary concept of God, whence it follows frat GOD is a limit concept.

There is, then, a clear sense in which God is unconceptualizable or unbegreiflich: he cannot be grasped by the use of any ordinary concept. But it doesn't follow that we have no concept of God. We do. The concept GOD is a limit concept: it is the concept of something that cannot be grasped using ordinary concepts. Our cognitive architecture is such that we can grasp only the general, the repeatable, but never the irreducibly singular. The concept GOD, however, is the concept of 'something' absolutely and irreducibly singular. God is one without a second, one without even the possibility of a second. Any god that doesn't satisfy this metaphysical exigency just isn't worth his salt.

The concept GOD is the concept of something that lies at the outer limit of discursive intelligibility, and indeed just beyond that limit. We can argue up to this Infinite Object/Subject, but then discursive operations must cease. We cannot penetrate the divine essence since this essence is one with existence, and existence cannot be conceptually penetrated. We can however point to God, in a manner of speaking, using limit concepts. The concept GOD is the concept of an infinite, absolute and wholly transcendent reality whose realitas formalis so exceeds our powers of understanding that it cannot be taken up into the realitas objectiva of any of our ordinary concepts.

Now if you have followed that, then you are in a position to see that the following objection is a 'cheap shot' easily dismissed. "You contradict yourself. You say that God cannot be conceptualized but at the same time you operate with a concept of God as unconceptualizable." But no contradiction arises once we distinguish ordinary from limit concepts.

If the critic accuses me of inventing a distinction ad hoc to save the ineffability and transcendence of God, then my reply will be that there are numerous other examples of limit concepts. See the aptly appellated category, Limit Concepts.

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*The term Grenzbegriff first enters philosophy in 1781 in Kant's Critique of Pure Reason. Curiously, he uses the term only once in the works he himself published. The term surfaces a few more times in his Nachlass. The sole passage in the published works is at A255/B311 where Kant remarks that the concept noumenon is a Grenzbegriff.

Singular Concepts Again

Ed writes,

Your counter-arguments are very useful but I find some of them puzzling. One argument that repeatedly occurs is that a concept cannot contain the object that it is a concept of. Our concept of Venus (if we have one) cannot contain Venus, for example.

My difficulty is that I agree with this argument, indeed it’s a cornerstone of the thesis in the book. See e.g.

The standard theory is a development of Mill’s theory, and is attended by the same difficulties. It explains properness by a semantic connection between proper name and bearer whereby the name can only signify that thing, but this leads to all the well-known difficulties mentioned in the last chapter, for example (i) how a large planetary body like Jupiter could be a part of a meaning or a thought, (ii) how identity statements involving different names for the same thing, such as “Hesperus is Phosphorus” can sometimes be informative, and (iii) how negative existential statements, which apparently deny a meaning for the name, are possible at all.

My emphasis. So where are we disagreeing I wonder? Is it that I claim a singular term has a meaning or sense? But in other posts of yours, you seem to agree that singular terms have a sense.

Or is it that you think that the sense of a singular term is ‘general’?

BV: Yes, that is what I claim. A singular term such as a name has a sense, but its sense is general. But I note that you switched from 'concept' to 'sense.' They are closely related. We may have to examine whether they are equivalent.

If so, you need to define what ‘general’ means. I define it as repeatable. A repeatable concept is one that we can without contradiction suppose to be instantiated by more than one individual, perhaps by individuals in different possible worlds. A singular concept by contrast is one where we cannot suppose repeatability without contradicting ourselves. For example, I cannot rationally entertain the thought that there could have been someone else who was Boris Johnson in 2021. That is because ‘someone else’ in this context means ‘someone other than Boris Johnson’, but ‘who was Boris Johnson’ means ‘someone who was no other than Boris Johnson’.

Thus to suppose that there could have been someone else who was Boris Johnson in 2021 is to suppose that there could have been someone who was both (1) other than Boris Johnson and (2) not other than Boris Johnson.

BV: I accept your definitions of 'general concept' and 'singular concept' pending some caveats to come. We agree that there are general concepts. We also agree that there are general terms and that there are singular terms. Presumably we also agree that a term is not the same as the concept the term expresses. The English word 'tree' and the German word 'Baum' are both token-distinct and type-distinct. But they express the same concept. Therefore, a word and the concept it expresses are not the same. And the same goes for sense: a word is not the same as its sense.

We disagree about whether there are singular concepts. You say that there are and I say that there aren't.

I think the onus is on you to establish that there cannot be unrepeatable concepts in the sense defined above.

BV: Why is the onus probandi on me rather than on you? Why is there a presumption in favor of your position that I must defeat, rather than the other way around? But let's not worry about where the burden of proof lies. We are not in a court room. You want an argument from me to the conclusion that there are no singular/individual/unrepeatable concepts. The demand is legitimate regardless of burden-of-proof considerations.

We agree that a first-level singular concept C, if instantiated, is instantiated by exactly one individual in the actual world and by the very same individual in every merely possible world in which C is instantiated. This is essentially your definition of 'singular concept.' I don't disagree with it but I say more.

I say that every concept is a mental grasping by the person who deploys the concept of the thing or things that instantiate (fall under, bear) the concept. A concept of an individual, then, would have to be a mental grasping of what makes that individual be the very individual it is and not some other actual or possible individual. So if there is the irreducibly singular concept Socrateity, then my deployment of that concept would allow we to grasp the haecceity (thisness) of Socrates which is precisely his and 'incommunicable' (as a schoolman might say) to any other individual actual or possible. But this is what minds of our type cannot grasp. Every concept we deploy is a general concept, and it doesn't matter how specific the concept is. Specificity no matter how far protracted never gets the length of singularity.

All of our concepts are mental representations of the repeatable features of things. It follows that all of our concepts are general. The individual, however, is essentially unrepeatable. For that very reason there cannot be a concept of the individual qua individual.

Consider Max Black's world in which there are exactly two iron spheres, alike in all monadic and relational respects, and nothing else. If there were an individual concept of the one sphere, then it would also be an individual concept of the other. But then it would not be an individual or singular concept: it would be general. It would be general because it would have two instances. The only way there could be two individual concepts is if each had as a constituent an iron sphere — which is absurd. Therefore, there cannot be any individual concepts.

A Proof of Individual Concepts?

This just in from Edward:

Proof that singular concepts (aka individual concepts) exist.

1. Common terms (‘cat’) and singular terms (‘this cat’, ‘Max’) exist.

2. These terms are meaningful, i.e. their meanings exist.

3. A concept is the meaning of a term.

4. Thus (from 1,2, 3) singular concepts, aka singular meanings, exist.

QED

This argument equivocates on 'meaning.' There are of course general and singular terms and they both have meanings if the meaning of a term is its extension, the (set of) things to which it applies. Accordingly, the meaning/extension of 'cat' is (the set of) cats, and the meaning/extension of 'Max' is Max, or his singleton. General terms also have meaning in the sense of intension. 'Cordate' and 'renate' are general terms that have the same extension but differ in intension. But the singular term 'Max,' while it has an extension, lacks an intension.

So for both (1) and (2) to be true, the meaning of a term must be its extension. But for (3) to be true, the meaning of a term must be its intension. So the argument trades on an equivocation and is for that reason invalid.

Here is a sound argument:

5. A concept is the intension of a term.

6. Singular terms lack intensions.

7. If a term lacks an intension, then there is no concept the term expresses.

Therefore

8. Singular terms do not express concepts. (From 5, 6, 7)

9. If a term does not express a concept, then there exists no concept the term expresses.

Therefore

10. There are no singular/individual concepts.

Just ask yourself: how could there be a concept of precisely Max and nothing actually or possibly different from Max? Suppose that there is a definite description that Max alone satisfies in the actual world. That description would express a concept that only one thing could bear or instantiate. But such a concept would not be singular but general since something else might have satisfied the description. For there to be an individual concept of Max, Max himself would somehow have to be a constituent of the concept. But that is impossible and for two reasons. First, concepts reside in the mind but no cat is a constituent of anything in my mind. Second, a concept is distinct from its bearer and can exist whether or not its bearer exists. But the concept MAX, if there were such a concept, would not be wholly distinct from its bearer and could not exist without its bearer.

The individual qua individual cannot be conceptualized. My conceptual grasp of an individual such as Max is always and necessarily by way of general concepts: cat, domestic cat, black cat, Tuxedo cat, black male Tuxedo cat five years old and weighing 20 lbs, cat presently in my visual field, this cat to which I am now pointing. Note that Max need not be this cat to which I am presently pointing, whence it follows that the haecceity of Max himself cannot be reached or grasped or conceptualized in the concept this cat to which I am presently pointing.

Intentionality, Singularity, and Individual Concepts

Herewith, some notes on R. M. Sainsbury, Intentionality without Exotica. (Exotica are those items that are "nonexistent, nonconcrete, or nonactual." (303) Examples include Superman and Arcadia.)

'Jack wants a sloop' could mean three different things. (a) There is a particular sloop Jack wants. In this case, Jack's desire is externally singular. Desire is an object-directed mental state, and in this case the object exists and is singular.

(b) There is no particular sloop Jack wants; what he wants is "relief from slooplessness" in Quine's phrase. In this case the desire, being "wholly non-specific," is not externally singular. In fact, it is not singular at all. Jack wants some sloop or other, but no particular sloop whether one that exists at present or one that is to be built.

(c) Jack wants a sloop of a certain description, one that, at the time of the initial desire, no external object satisfies. He contracts with a ship builder to build a sloop to his exact specifications, a sloop he dubs The Mary Jane. It turns out, however, that the sloop is never built. In this case, Sainsbury tells us, the desire is not externally singular as in case (a), but internally singular:

The concept The Mary Jane that features in the content of the desire is the kind of concept appropriate to external singularity, though that kind of singularity is absent, so the desire counts as internally singular. The kind of concept that makes for singularity in thought is one produced by a concept-producing mechanism whose functional role is to generate concepts ﬁt for using to think about individual things. I call such a concept an ‘‘individual concept’’ (Sainsbury 2005: 217ff). Individual concepts are individuated by the event in which they are introduced. In typical cases, and when all goes well, an act of attention to an object accompanies, or perhaps is a constituent of, the introduction of an individual concept, which then has that object as its bearer. In cases in which all does not go well, for example in hallucination, an individual concept is used by the subject as if it had an object even though it does not; an act internally indistinguishable from an act of attending to an object occurs, and in that act an individual concept without a bearer comes into being. A concept so introduced can be used in thought; for example an individual concept C can be a component in wondering whether C is real or merely hallucinated. In less typical cases, it is known to the subject that the concept has no bearer. An example would be a case in which I know I am hallucinating.

External singularity is relational: a subject is related to an object. Internal singularity is not relational in this way. (301, bolding added.)

What interests me here is the notion of an individual concept (IC). We are told above that an IC is distinct from its bearer and can exist without a bearer. So the existence and identity of an IC does not depend on its having a bearer. We are also told that one and the same IC can figure in both a veridical and a non-veridical (hallucinatory) experience, the seeing of a dagger, say. So it is not the bearer that individuates the IC. What individuates it is the mental event by which it is introduced.

To these two points I add a third: it is built into the sense of 'individual concept' that if an individual concept C has a bearer, then it has exactly one bearer in the actual world, and the same bearer in every possible world in which it has a bearer. So if there is an individual concept SOCRATES, and it has a bearer, then it has exactly one bearer, Socrates, and not possibly anything distinct from Socrates. This implies that individual concepts of externally singular items are as singular in content as the items of which they are the concepts. This in turn implies that no individual concept of an externally singular item is general: no such concept is multiply instantiable or multiply 'bearable.'

I now add a fourth point: concepts are mental entities in the sense that they cannot exist apart from minds. Concepts are representations and therefore mental entities in the sense indicated. A fifth point is that our minds are finite and our powers of conceptualization correspondingly limited. One obvious limit on our power to conceptualize is that no concept of ours can capture or grasp the haecceity (thisness) of any externally singular item. We ectypal intellects cannot conceptually eff the ineffable, where what is ineffable is the individual in its individuality or singularity or haecceity, i.e., in that which makes it be this individual and no other actual or possible individual. God, the archetypal intellect, may be able to grasp the haecceity of an individual, but this is clearly beyond our 'pay grade.' If God can do it, this is presumably because he creates the individual ex nihilo.

It follows from the fourth and fifth points that all of our concepts are general. Suppose that the concept FASTEST MARATHONER (FM) applies to Jones. That concept is general despite the fact that at any given time t only one person can instantiate or bear it. For at times earlier and later than t, some other runners were and will be the FM. Therefore, FM does not capture Jones' haecceity. But even if Jones is the FM at every time in the actual world, there are possible worlds in which some other person is the FM at every time. What's more, at any time at which Jones is the FM, he might not have been the FM at that time.

Sainsbury's theory of individual concepts strikes me as incoherent. The following cannot all be true:

1) There are individual concepts.

2) Concepts are representations in finite minds, and our minds are finite.

3) Individual concepts of externally singular items must be as singular in content as the items of which they are the concepts.

4) Every externally singular item exists. (There are no 'exotica.')

5) Every externally singular item is wholly determinate or complete where x is complete =_df x satisfies the property version of the Law of Excluded Middle (tertium non datur).

6) No concept in a finite mind of an externally singular item is singular in content in the sense of encoding every property of the wholly determinate or complete thing of which it is the concept.

7) One and the same individual concept can figure in both a veridical and a non-veridical (hallucinatory) experience.

Sainsbury is committed to each of these seven propositions, and yet they cannot all be true. The first five propositions, taken in conjunction, entails the negation of (6). Or if (6) is true, then (1) is false. (6) and (7) cannot both be true.

I conclude that there are no individual concepts, and that the distinction between externally singular and internally singular object-directed mental states cannot be upheld.

Why I Reject Individual Concepts

This entry was first posted on 24 July 2011. Time for a repost with minor modifications. I find that I still reject individual concepts. Surprise!

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Consider the sentences 'Caissa is a cat' and 'Every cat is an animal.' Edward the Nominalist made two claims in an earlier comment thread that stuck in my Fregean craw:

1) The relation between 'Caissa' and 'cat' is the same as the relation between 'cat' and 'animal'.

2) The relation between *Caissa* and *cat* is the same as the relation between *cat* and *animal.*

Single quotes are being used in the usual way to draw attention to the expression enclosed within them. Asterisks are being used to draw attention to the concept expressed by the linguistic item enclosed within them. I take it that we agree that concepts are mental in nature in the sense that, were there no minds, there would be no concepts.

Affirming (2), Edward commits himself to individual or singular concepts. I deny that there are individual concepts and so I reject (2). Rejecting (2), I take the side of the Fregeans against the traditional formal logicians (TFL-ers) who think that singular propositions can be analyzed as general. Thus 'Caissa is a cat' gets analyzed by the TFL-ers as 'Every Caissa is a cat.'

To discuss this profitably we need to agree on the following definition of 'individual concept':

D1. C is an individual concept of x =_df x is an instance of C, and it is not possible that there be a y distinct from x such that y is an instance of C.

So if there is an individual concept of my cat Caissa, then Caissa instantiates this concept and nothing distinct from Caissa does or could instantiate it. We can therefore say that individual concepts, if there are any, 'capture' or 'grasp' or 'make present to the mind' the very haecceity (non-qualitative thisness) of the individuals of which they are the individual concepts.

We can also speak of individual concepts as singular concepts and contrast them with general concepts. *Cat* is a general concept. What makes it general is not that it has many instances, although it dos have many instances, but that it can have many (two or more) instances. General concepts are thus multiply instantiable.

The concept C1 expressed by 'the fattest cat that ever lived and ever will live' is also general. For, supposing that Oscar instantiates this concept, it is possible that some other feline instantiate it. Thus C1 does not capture the haecceity of Oscar or of any cat. C1 is general, not singular. C1 is multiply instantiable in the sense that it can have two or more instances, though not in the same possible world or at the same time.

And so from the fact that a concept applies to exactly one thing if it applies to anything, one cannot validly infer that it is an individual or singular concept. Such a concept must capture the very identity or non-qualitative thisness of the thing of which it is a concept. This is an important point. To push further I introduce a definition and a lemma.

D2. C is a pure concept =_df C involves no specific individual and can be grasped without reference to any specific individual.

Thus 'green,' 'green door,' 'bigger than a barn,' 'self-identical,' and 'married to someone' all express pure concepts. 'Taller than the Washington Monument,' 'married to Heidegger,' and 'identical to Heidegger' express impure concepts, if they express concepts at all.

Lemma 1: No individual concept is a pure concept.

Proof. By (D1), if C is an individual concept of x, then it is not possible that there be a y distinct from x such that y instantiates C. But every pure concept, no matter how specific, even unto maximal specificity, is possibly such as to have two or more instances. Therefore, no individual concept is a pure concept.

Consider the famous Max Black example of two iron spheres alike in all monadic and relational respects. A pure concept of either, no matter how specific, would also be a pure concept of the other. And so the non-qualitative haecceity of neither would be captured by that pure concept.

Lemma 2. No individual concept is an impure concept.

Proof. An individual concept is either pure or impure. If C is impure, then by (D2) it must involve an individual. And if C is an individual concept it must involve the very individual of which it is the individual concept. But individuum ineffabile est: no individual can be grasped precisely as an individual. But that is precisely what one would have to be able to do to have an impure concept of an individual. Therefore, no individual concept is an impure concept.

Putting the lemmata together, it follows that an individual concept cannot be either pure or impure. But it must be one or the other. So there are no individual concepts. Q. E. D.!